If A : B = 2 : 3, B : C = 2 : 3 and C : D = 3 : 4, then A : D = ?

Correct option is C

Given:

A : B = 2 : 3
B : C = 2 : 3
C : D = 3 : 4

Solution:
A : B = 2 : 3
B : C = 2 : 3
Make B equal in both

LCM of 3 and 2 = 6
So rewrite:
A : B = 4 : 6
B : C = 6 : 9
So A : B : C = 4 : 6 : 9

C : D = 3 : 4

C = 9 in previous ratio, so scale to match
Multiply C : D = 3 : 4 by 3

C : D = 9 : 12
So A : B : C : D = 4 : 6 : 9 : 12

A : D = 4 : 12 = 1 : 3